Home/Chain Registry/Block #143,014

Block #143,014

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/31/2013, 8:49:28 AM · Difficulty 9.8374 · 6,646,718 confirmations

2CC

Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header

Block Hash

a96af91e7bdc6772b15b568b761854baf83770233e1c195047a53b8be2ec5007

View on Chainz ↗

Height

#143,014

Difficulty

9.837363

Transactions

Size

197 B

Version

Bits

09d65d73

Nonce

110,998

Timestamp

8/31/2013, 8:49:28 AM

Confirmations

6,646,718

Merkle Root

8980d8587bb6babdd01ab5968eca1511009b8829a46558215ad454f786c908dd

Transactions (1)

Coinbase8980d8587bb6ba…d454f786c908dd

1 in → 1 out10.3200 XPM109 B

AbTCWeS3…w6n6BGqp

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.211 × 10⁹⁰(91-digit number)

12116997288684134884…84046481983611070720

Discovered Prime Numbers

p_k = 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin + 1

1.211 × 10⁹⁰(91-digit number)

12116997288684134884…84046481983611070721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.423 × 10⁹⁰(91-digit number)

24233994577368269768…68092963967222141441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.846 × 10⁹⁰(91-digit number)

48467989154736539537…36185927934444282881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.693 × 10⁹⁰(91-digit number)

96935978309473079074…72371855868888565761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.938 × 10⁹¹(92-digit number)

19387195661894615814…44743711737777131521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.877 × 10⁹¹(92-digit number)

38774391323789231629…89487423475554263041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.754 × 10⁹¹(92-digit number)

77548782647578463259…78974846951108526081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.550 × 10⁹²(93-digit number)

15509756529515692651…57949693902217052161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.101 × 10⁹²(93-digit number)

31019513059031385303…15899387804434104321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.203 × 10⁹²(93-digit number)

62039026118062770607…31798775608868208641

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page →

★★☆☆☆

Rarity

UncommonChain length 10

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 143014

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock a96af91e7bdc6772b15b568b761854baf83770233e1c195047a53b8be2ec5007

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #143,014 on Chainz ↗